te to many others. Moreover, the methods of reasoning,
which he does adopt, will be of a peculiar kind, suited to the nature
of childhood, the results being mainly intuitional, rather than the
fruits of formal logic. To oblige a young child to go through a formal
syllogistic statement in every step in elementary arithmetic, for
instance, is simply absurd. It makes nothing plain to a child's mind
which was not plain before. On the contrary, it often makes a muddle of
what had been perfectly clear. What was in the clear sunlight of
intuition, is now in a haze, through the intervening medium of logical
terms and forms, through which he is obliged to look at it.

A primary teacher asks her class this question: "If I can buy 6 marbles
with 1 penny, how many marbles can I buy with 5 pennies?" A bright boy
who should promptly answer "30" would be sharply rebuked. Little
eight-year old Solon on the next bench has been better trained than
that. With stately and solemn enunciation he delivers himself of a
performance somewhat of this sort. "If I can buy 6 marbles with 1 penny,
how many marbles can I buy with 5 pennies? Answer--I can buy 5 times as
many marbles with 5 pennies as I can buy with 1 penny. If, therefore, I
can buy 6 marbles with 1 penny, I can buy 5 times as many marbles with 5
pennies; and 5 times 6 marbles are 30 marbles. Therefore, if I can buy 6
marbles with one penny, I can buy 30 marbles with 5 pennies."

And this is termed reasoning! And to train children, by forced and
artificial processes, to go through such a rigmarole of words, is
recommended as a means of cultivating their reasoning power and of
improving their power of expression! It is not pretended that children
by such a process become more expert in reckoning. On the contrary,
their movements as ready reckoners are retarded by it. Instead of
learning to jump at once to the conclusion, lightning-like, by a sort of
intuitional process, which is of the very essence of an expert
accountant, they learn laboriously to stay their march by a cumbersome
and confusing circumlocution of words. And the expenditure of time and
toil needed to acquire these formulas of expression, which nine times
out of ten are to those young minds the mere _dicta magistri_, is
justified on the ground that the children, if not learning arithmetic,
are learning to reason.

Let me not be misunderstood. I do not advocate the disuse of
explanations. Let teachers explain, let children